Thick inorganic shells endow colloidal nanocrystals (NCs) with enhanced photochemical stability and suppression of photoluminescence intermittency (also known as blinking). However, the progress of using thick-shell 100 90 heterostructure NCs in applications has been limited due to the low photoluminescence quantum yield (PL QY <= 60%) at room temperature. Here, we demonstrate thick-shell NCs with CdS/CdSe/CdS seed/spherical quantum well/shell (SQW) geometry that exhibit near-unity PL QY at room temperature and suppression of blinking. In SQW NCs, the lattice mismatch is diminished between the emissive CdSe layer and the surrounding CdS layers as a result of coherent strain, which suppresses the formation of misfit defects and consequently permits, similar to 100% PL QY for SQW NCs with a thick CdS shell (>5 nm). High PL QY of thick-shell SQW NCs is preserved even in concentrated dispersion and in film under thermal stress, which makes them promising candidates for applications in solid-state concentrators.